Napoleon's military priority, on becoming first consul in 1799, is to reverse gains recently made by Austria during his absence on the Egyptian campaign. To give himself a freer hand he makes a tentative offer of peace to England in December 1799, but it is firmly rejected.

As in 1796, the Austrians could be attacked by French armies either north of the Alps in Germany or south of them in Italy. No doubt remembering his own triumphs in that year, Napoleon selects Italy. He hopes to surprise the enemy by bringing his army south through the Great St Bernard pass in May 1800 before the snows have cleared. He himself slithers through the pass on a mule, but this does not deter the painter Jacques-Louis David from depicting him on a magnificent rearing stallion among the snowy peaks.

When the crucial encounter with the Austrians occurs, at Marengo on June 14, it is very nearly a disaster for Napoleon. By mid-afternoon it seems that the Austrians have won the day. But a brave French counter-attack reverses the situation.

Victory at Marengo is followed by an armistice and a truce - which Napoleon breaches in November, when he sends a French army north of the Alps against Vienna. Another French victory, at Hohenlinden in December, prompts the Austrian emperor to sign a treaty at Lunéville in February 1801. It goes even beyond the terms of Campo Formio. France keeps the Rhineland. Austria recognizes the four French sister republics.

Napoleon against Britain: 1800-1802

The conflict between France and Britain, continuously at war since 1793, tends always towards stalemate. The two nations are evenly matched but have very different strengths. Britain has a much smaller population (11 million compared to 27 million in France in 1801). This disadvantage is offset by Britain's wealth (from a more developed economy and extensive overseas trade) and by the British superiority at sea. In 1803 France has 23 ships of the line; Britain has 34 in service and another 77 in reserve.

For these reasons the British contribution to any war against France in continental Europe is largely limited to providing funds for allied armies.

The naval clash between Britain and France is a strange one - not so much a sea war as a coast war. It is the permanent concern of the British navy, commanding the seas, to harm France and her allies by preventing any merchant ships other than those of Britain from reaching continental ports. And it is the permanent concern of the French armies, commanding the land, to prevent British vessels entering those same ports.

Third parties suffer as much as anyone from this form of economic warfare, particularly after Britain adopts the policy of seizing goods carried by the ships of neutral nations if they are destined for a harbour under blockade.

Indignation at this British policy, heightened by diplomatic pressure from Napoleon, prompts Russia, Sweden and Denmark to form in December 1800 a League of Armed Neutrality. They declare the Baltic ports out of bounds to British ships. The embargo is strengthened when the Danes seize Hamburg, the main harbour for British trade with the German states.

Britain responds by sending a naval fleet into the Baltic. The second-in-command is Nelson, who sails into shallow and well-defended waters in Copenhagen harbour. There is heavy fighting, during which the commander of the fleet flies the signal for Nelson to withdraw (this is the famous occasion when he puts the telescope to his blind eye).

Nelson destroys many of the ships in the harbour and damages the shore defences in this battle of Copenhagen (2 April 1801). His victory prompts the Danes to make peace in May. Sweden does so in the same month, and Russia follows suit in June.

By now, as after Campo Formio, Britain and France are the only two nations still at war. From the British point of view one affront still needs to be righted. In March 1801 a fleet is sent through the Mediterranean to help the Turks expel the French from Egypt. The French command in Cairo surrenders in June, followed by Alexandria in August.

Both sides are now exhausted. There have been tentative peace talks since February. Terms are agreed in October, putting an end to hostilities. The peace is signed in Amiens in March 1802.

Napoleon's negotiators do well for France. All overseas territories taken by Britain in the past nine years (including several West Indian islands) are returned into French hands. Similarly Minorca reverts to Spain and the Cape colony in South Africa to Holland. But Britain keeps Sri Lanka (taken from the Dutch) and Trinidad (previously Spanish). Egypt is to be Turkish again. Malta (taken by Napoleon in 1798 and by Britain in 1800) is to be restored to the Knights of St John.

The peace of Amiens: 1802-1803

Peace is eagerly greeted by Europeans starved of the pleasures of travel - particularly the British, cooped up in their island for years, who now flock across the Channel to enjoy once again the pleasures of Paris. But this is to prove only a breathing space. Nothing has been resolved in the long rivalry between Britain and France, and each government soon finds much to complain about in the behaviour of the other during the interlude of peace.

Napoleon annoys the British by failing to allow the spirit of harmony into the market place. His refusal to agree a commercial treaty means that British merchants are penalized by high tariffs in French and allied ports. They conclude that peace seems no more profitable than war.

Meanwhile Napoleon alarms the British government by his expansionist behaviour in regions not covered by the treaty - for example in his annexation of Piedmont in 1802, to bridge the gap between France and the Cisalpine republic.

Britain gives France more specific cause for complaint by not fulfilling the terms of the treaty of Amiens. It has been agreed that she will withdraw from Malta. Her failure to do so would be justified in modern eyes by the expressed views of the Maltese. Horrified at the prospect of the return of the Knights of St John, the local assembly passes a resolution inviting George III to become their sovereign on condition that he maintains the Roman Catholic faith in the island.

However, the wishes of local inhabitants carry little weight in diplomatic negotiations in the early 19th century. And Britain, remaining in possession of the island, is undoubtedly in violation of the treaty.

Napoleon complains but avoids pressing the issue to the brink of hostilities. It is likely that his long-term intentions towards Britain are not peaceful, but he is not yet ready for a renewal of war. He needs time, in particular, to build up his fleet. The same logic makes Britain prefer an early renewal of the conflict. For no very good reason, other than long-term self-interest, the British government declares war on France in May 1803.